Question: Let $f(x) = -7x^{2}+8x+10$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-7x^{2}+8x+10 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -7, b = 8, c = 10$ $ x = \dfrac{-8 \pm \sqrt{8^{2} - 4 \cdot -7 \cdot 10}}{2 \cdot -7}$ $ x = \dfrac{-8 \pm \sqrt{344}}{-14}$ $ x = \dfrac{-8 \pm 2\sqrt{86}}{-14}$ $x =\dfrac{-4 \pm \sqrt{86}}{-7}$